Virtual Topography Measurement with Transfer Functions Derived by Fitted Time Series Models

The deviations between the actual geometry of a workpiece and the measured geometry are defined by the transfer function of the surface topography measuring instrument used. When the transfer characteristics of a measuring instrument are known, they can, for example, be used for the estimation of measuring results by performing virtual measurements and can subsequently be applied for the estimation of the measurement uncertainty. A technique that has been increasingly applied for the determination of the transfer function of topography measuring devices is the approach based on physical modeling. Here, mathematical models apply simplifications of the complex physical relationships to describe the transfer characteristics of measuring devices. Another method used in practice is the application of material measures for the direct measurement of transfer properties. Within this paper, an alternative approach developed by the authors that applies the ARMA model is further investigated and optimized with regard to its practical applicability. This model was described in a previous publication (Keksel et al 2018 Meas. Sci. Technol. 29 095012) and combines the advantages of theoretical modeling and the experimental determination of transfer characteristics. Within the present work, the approach is further optimized and it is demonstrated that the description of measuring devices by the ARMA model delivers reasonable results for various measuring principles that can be used for a precise virtual prediction of measurement results.